EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. SOLUTION The radius is 3 and the center is at the origin. x 2 + y 2 = r.

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Presentation transcript:

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. SOLUTION The radius is 3 and the center is at the origin. x 2 + y 2 = r 2 x 2 + y 2 = 3 2 x 2 + y 2 = 9 Equation of circle Substitute. Simplify. ANSWER The equation of the circle is x 2 + y 2 = 9

EXAMPLE 2 Write the standard equation of a circle Write the standard equation of a circle with center (0, –9) and radius 4.2. SOLUTION (x – h) 2 + ( y – k) 2 = r 2 (x – 0) 2 + ( y – (–9)) 2 = x 2 + ( y + 9) 2 = Standard equation of a circle Substitute. Simplify.

GUIDED PRACTICE for Examples 1 and 2 Write the standard equation of the circle with the given center and radius. SOLUTION (x – h) 2 + ( y – k) 2 = r 2 (x – 0) 2 + ( y – (0)) 2 = x 2 + y 2 = 6.25 Standard equation of a circle Substitute. Simplify. 1. Center (0, 0), radius 2.5

GUIDED PRACTICE for Examples 1 and 2 Write the standard equation of the circle with the given center and radius. SOLUTION (x – h) 2 + ( y – k) 2 = r 2 (x –(–2)) 2 + ( y – 5) 2 = 7 2 Standard equation of a circle Substitute. 2. Center (–2, 5), radius 7 (x + 2) 2 + ( y – 5) 2 = 49 Simplify.